Theorem tpcomb 4756

Description: Swap 2nd and 3rd members of an unordered triple. (Contributed by NM, 22-May-2015.)

Assertion

Ref	Expression
tpcomb	⊢ {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵}

Proof of Theorem tpcomb

Step	Hyp	Ref	Expression
1		tpcoma 4755	. 2 ⊢ {𝐵, 𝐶, 𝐴} = {𝐶, 𝐵, 𝐴}
2		tprot 4754	. 2 ⊢ {𝐴, 𝐵, 𝐶} = {𝐵, 𝐶, 𝐴}
3		tprot 4754	. 2 ⊢ {𝐴, 𝐶, 𝐵} = {𝐶, 𝐵, 𝐴}
4	1, 2, 3	3eqtr4i 2773	1 ⊢ {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵}

Syntax hints:   = wceq 1537  {ctp 4635

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3or 1087  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-un 3968  df-sn 4632  df-pr 4634  df-tp 4636

This theorem is referenced by:  f13dfv  7294  frgr3v  30304  signswch  34555  signstfvcl  34567  dvh4dimN  41430